MEL IKE YILMAZ _ PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION M.S. Thesis MELIKE_ YILMAZ 2017 IS¸IK UNIVERSITY 2017 PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION MELIKE_ YILMAZ B.S., Industrial Engineering, IS¸IK UNIVERSITY, 2015 Submitted to the Graduate School of Science and Engineering in partial fulfillment of the requirements for the degree of Master of Science in Industrial Engineering Operations Research IS¸IK UNIVERSITY 2017 IS¸IK UNIVERSITY GRADUATE SCHOOL OF SCIENCE AND ENGINEERING PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION MELIKE_ YILMAZ APPROVED BY: Assist. Prof. Dr. S. Tankut Atan I¸sıkUniversity (Thesis Supervisor) Assoc. Prof. Dr. S. C¸a˘glarAksezer I¸sıkUniversity (Thesis Co-Supervisor) Assist. Prof. Dr. Demet O.¨ Unl¨uakın¨ I¸sıkUniversity Assist. Prof. Dr. Burak C¸avdaro˘glu Kadir Has University APPROVAL DATE: ..../..../.... PREDICTION OF FINAL FOOTBALL LEAGUE STANDINGS BY DYNAMIC FRONTIER ESTIMATION Abstract Data Envelopment Analysis (DEA) is a commonly used method for efficiency assessment of teams in many sports including football. In this work, we investigate how estimations of final league standings with DEA efficiency measures evolve as the season progresses using Turkish first division football league data for five seasons. After the conclusion of each week, a DEA analysis is run using available data until then, and computed efficiencies are used to estimate the final table standings. While the estimates fluctuate early in the season, they tend to stabilize after several weeks. Tracking the weekly progress of the results may give the teams a chance to finish in a better position by focusing on their inefficiencies. Furthermore, the choice of the DEA linear programming model makes a difference in the quality of the results. Estimations are improved by using a model that incorporates expert knowledge about football. Keywords: Data Envelopment Analysis (DEA), Assurance Region Model, Football Efficiency, Turkish Football Clubs ii DINAM_ IK_ ONC¨ U¨ METOTLAR KULLANARAK FUTBOL LIG_ IN_ IN_ PUAN SIRALAMASININ TAHMIN_ I_ Ozet¨ Veri Zarflama Analizi (VZA) metodu, futbol dahil olmak ¨uzerebir¸coktakım sporunun verimlilik de˘gerlendirmesi i¸cinyaygın olarak kullanılmaktadır. Bu ¸calı¸s- mada, T¨urkiye'de birinci ligde oynayan futbol takımlarının performansları son be¸syıllık ger¸cekveri ile analiz edilip de˘gerlendirilmektedir. C¸alı¸smanın amacı, performans ¨ozelliklerini kullanarak lig sonunda olu¸sması muhtemel sıralamayı sezon i¸cerisindeolabildi˘ginceerken tahmin etmektir. Sezonun ba¸sındaki tah- min do˘grululuk oranı d¨u¸s¨ukolurken, sezon haftaları ge¸ctik¸cekayda de˘gerse- viyelere ¸cıkmaktadır. Yapılan haftalık analizler sonrasında, her karar noktası yani takımın etkinlik de˘gerihakkında bilgiler elde edilmektedir. Bu bilgiler kul- lanılarak takımların zayıf y¨onleriney¨onelikhamleler yapması ve sezonu daha iyi bir sırada bitirmesi m¨umk¨unolacaktır. Anahtar kelimeler: Veri Zarflama Analizi (VZA), G¨uven B¨olgesi (AR) Y¨ontemi, Futbol Verimlili˘gi,T¨urkiye Futbol Kul¨upleri iii Acknowledgements First of all, I would like to give special thanks to my thesis supervisor Assist. Prof. S. Dr. Tankut Atan for his great concern, patience, kind support and guidance. I would like to also give special thanks to my thesis co-supervisor Assoc. Prof. S. Dr. C¸a˘glarAksezer, for his never ended patience, support and guidance. It was pleasure working with them during my master studies. Additionally, I would like to also thank all other faculty members of I¸sıkUniversity Industrial Engineering Department for their support during my bachelor and master studies. Special appreciation goes to my friends and colleagues who have provided support to me in completing my study. Also, I am extremely gratefully to thank to my parents G¨uzideYılmaz, Umit¨ Yılmaz, Umit¨ Can Yılmaz and S¸ehnaz Ozel¨ for their never ended trust, patience and endless encouragement. iv To my family and friends. Table of Contents Abstract ii Ozet¨ iii Acknowledgements iv List of Tables vii List of Figures viii List of Abbreviations ix 1 Introduction 1 2 Literature Review 4 3 Data 11 4 Methodology 15 4.1 Data Envelopment Analysis (DEA) . 15 4.2 Analytic Hierarchy Process (AHP) . 22 5 Results 27 5.1 Financial Data . 34 6 Conclusion 36 Reference 39 Appendices 45 A 46 A.1 Data . 46 A.2 Analytic Hierarchy Process . 52 A.3 Pearson Correlation Coefficients Results . 56 List of Tables 2.1 Review of the literature on performance assessment of football teams using DEA. .7 2.2 Review of the literature on performance assessment of basketball and handball teams using DEA. .8 2.3 Review of the literature on performance assessment of tennis and olympic games using DEA. .9 2.4 Review of the literature on performance assessment of baseball, handball and golf teams using DEA. 10 3.1 Descriptive statistics. 14 4.1 Results of a numerical example from 2015-2016 season. 20 4.2 Saaty's nine-point scale for relative importance. 22 4.3 Geometric mean matrix. 23 4.4 Normalized matrix. 23 4.5 Priorities of the inputs by the experts. 26 4.6 Assurance Region lower and upper bounds for input ratios. 26 5.1 Descriptive statistics of CCR and AR models. 31 5.2 Descriptive statistics of financial data. 35 A.1 Sample data. Week 34 in 2011-2012. 46 A.2 Sample data. Week 34 in 2012-2013. 47 A.3 Sample data. Week 34 in 2013-2014. 48 A.4 Sample data. Week 34 in 2014-2015. 49 A.5 Sample data. Week 34 in 2015-2016. 50 A.6 Correlation coefficient matrix. 51 A.7 Comparison matrix for the inputs by Expert 1. 52 A.8 Comparison matrix for the inputs by Expert 2. 52 A.9 Comparison matrix for the inputs by Expert 3. 53 A.10 Comparison matrix for the inputs by Expert 4. 53 A.11 Comparison matrix for the inputs by Expert 5. 54 A.12 Random Index Table. 54 A.13 Regression on rank: Final league standings vs. DEA estimations (R-square %) results. 56 A.14 Regression on rank: Weekly league standings vs. DEA estimations (R-square %) results. 57 vii List of Figures 4.1 Efficiency graph of 2015-2016 season. 21 5.1 Regression on rank: Final league standings vs. DEA estimations. 30 5.2 Weekly vs. final league rank estimation. 32 5.3 Progress of DEA scores for various cases. 33 5.4 Financial analysis of football teams for five seasons. 34 A.1 AHP questionnaire. 55 viii List of Abbreviations AHP Analytical Hierarcy Process AR Assurance Region AR-I-C Input Oriented Assurance Region Model CCR Charnes Cooper Rhodes CCR-I Input Oriented Charnes Cooper Rhodes Model CI Consistency Index CR Consistency Ratio CRS Constant Returns to Scale DEA Data Envelopment Analysis DMU Decision Making Unit LP Linear Programming NBA National Basketball Association NFL National Football League RI Random Consistency Index SFA Stochastic Frontier Analysis TFF Turkish Football Federation UEFA Union of European Football Associations VRS Variable Returns to Scale ix Chapter 1 Introduction Besides being the most popular sport in terms of followers and fans, football is a multibillion dollar industry that dominates the sports economics. Without doubt, European football clubs and managing bodies are the prominent stakeholders of this industry. Szymanski [1] provides a diverse collection of challenges faced in this arena since early 90's, especially focused on Euro area. European football holds several financial earning records for any professional sport on the face of the planet. According to Harris [2] , United Kingdom (UK) Premier League is the most broadcasted league in the world with earnings from TV rights of more than $2.5 billions per year being second best only after NFL. It also holds several top spots in the list of international clubs with most expensive sponsorship deals signed. Teams from UK and Spain are earning vast sums of money from selling their jersey and arena naming rights. More importantly, record amount of prize money is distributed to competitor clubs through organizations such as European Football Associations (UEFA) Champions League with total prize money well over billion dollars. In order to get a larger slice of the cake, teams try to achieve higher international recognition and dominance over each other. Consecutive appearances in inter- national organizations is the major key to this success. Teams qualify for such organizations when they secure a certain top spot in their final national league 1 standing. Turkish national league, which is named "Spor Toto S¨uper Lig", con- tains 18 top division clubs. A total 34 home and away games are played by each team with a Federation Cup tournament. Champion of the league is directly qual- ified for UEFA Champions League; the runner up should plays certain rounds of qualification matches. A certain number of consecutive seeders are qualified for the UEFA Europa League, which is the other international organization with slightly less prestige and financial earnings. Turkey's football industry gained critical acclaim during recent years as it im- proves drastically in terms of financial winning and losses. An in-depth historical background of Turkish football is provided by Senyuva and Tunc [3]. Clubs have earned large amounts of money from the sale of broadcasting rights and gained higher fan attendance as the construction of new generation stadiums completed. On the other hand, they also faced massive budgetary deficits because of oper- ating losses mainly occurring from astronomic transfer fees. Some of the clubs were even banned from international organizations because of the regulatory fi- nancial play rules. Some studies suggest that these economical factors have socio- psychological impacts on the society as well. Berument and Y¨ucel[4] provide the statistical basis of relation between Turkish industrial production performance and field performance of the country's most popular club, Fenerbah¸ceSK.